Questions tagged [frequency-response]

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system.

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511 views

Phase contribution of complex poles

I am struggling with understanding the phase contribution of each individual pole. Let's say we have a system (minimum-phase system if it makes a difference) and it has poles located at: and What is ...
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Nyquist Plot for transfer functions with poles at the origin

I'm learning Nyquist plots and something has been seriously bugging me when treating poles or zeros in the origin. Nyquist plots obtains information based on the argument principle which states "If f(...
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MATLAB - How do I get the Filter Function to get the output Energy Spectrum?

The image was from a question I posted on reddit, so ignore the title. I'm trying to write a program that plots these graphs I know that the first plot is just a plot of the source-signal so the "...
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Could someone please explain how to get frequency response of a given Bode Plot?

Having trouble with bode plots. I understand that the is to be converted to $dB$ but after that I'm stuck. Could someone please show me how this graph gives a frequency response of $10/1+jw10$
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Discrete Time Fourier Analysis

Suppose we're given the following: $ x[n] = 2 + (-1)^n $, and are given the impulse response $ h[n] = u[n] a^n $, of an LTI system where $ |a| < 1$. We're asked to find the output $y[n]$, if $x[n]$...
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Digital filter design of time series for specified frequency response function

I am currently working with vibration measurements in structures. In the netherlands there is a guideline for verifying vibration measurements for damage to machinery. This is the so-called "SBR ...
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finding phase and group delay from frequency response

(From Schaum's Outlines, DSP, second edition, problem 5.25, second part of problem) What's the procedure to find the Phase and Group Delay of: $$ H(e^{j\omega}) = e^{-j\theta}\left( \frac{e^{-j(\...
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Numerical Calculation of impulse response out of frequency response

Currently I work on my Masterthesis which deals with structural dynamic simulation. As a part of it I have to filter a Signal with a FIR-Filter. From that Filter I know the Frequency Response (picture)...
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What exactly is Savitzky-Golay differentiation filter?

I could understand Savitzky-Golay filter as being smoothing filter, but then there also seems to be Savitzky-Golay differentiation filter, though for some reason, details do not seem to be clear. So ...
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166 views

Sensor rise time compared to experimental step input rise time

I have a dynamic calibration system. With it, I am applying a experimental step input to a pressure sensor. The goal is to measure the step response of the sensor and use it to calculate the frequency ...
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Is it wrong to first calculate the whole system's Frequency response and then apply input to it?

Having a system like below, which (i think) is LTI, and $H(e^{j\omega}) = \begin{cases} 1 & |\omega|\leq \frac{\pi}{2} \\ 0 & |\omega| \gt \frac{\pi}{2} \end{cases} $ I've ...
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Frequency response of numerical differentiation by polynomial interpolation / finite difference

One can use polynomial interpolation (or finite difference) to do numerical differentiation. However, there seems to be a surprising lack of interest in obtaining frequency response of this numerical ...
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system identification: MATLAB tfestimate gives different results for different Fs

So I have an experimental data; A is a chirp signal (sweep sine wave) and B is the response of the system. I identify the system as follows in MATLAB: ...
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211 views

Computation of parameter filter to match a given frequency response

I'm looking for the practical way to compute the parameters ($a_1$, $a_2$) of a digital filter to match a certain frequency response. I'm studying the 12-poles filter of the vintage component SP0256 ...
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196 views

what happens If I change the phase and magnitude of a signal

I have a speech signal. I want to know what happens when I make some changes on the phase of its frequency reaponse. When I set its phase to zero I observed that the new signal is even and the ...
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555 views

How to prove these two definitions of the minimum phase transfer function are same?

There are so many definitions of the minimum phase transfer function, and these are two of them. The transfer function of the system which has no zeros or poles at right half plane. The transfer ...
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Given a plot of both the magnitude $|H(\omega)|$ and its angle, How can you find the $H(\omega)$?

I'm specifically trying to use an inverse Fourier Transform to find $h(t)$, but I'm finding it difficult to get $H(\omega)$ in the first place. I'm under the impression from my textbook that $H(\...
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Why the frequency response plots (of causal filters) only show positive frequency?

Take an example of the below plot for an LPF (Source : WikiPedia) The plot starts from $0$. We know that the fourier transform of any signal brings in negative frequencies due to complex exponentials ...
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How do I plot the square of the amplitude response?

I have calculated the transfer function of an FIR filter $$ y[n] = x[n] + α · x[n − R] $$ This is what I have $$ H(z) = 1 + αz^{-R} $$ Now I should plot the square of the amplitude response. So I ...
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Get the frequency response curve from FIR filter coefficients + sampling rate

What's the fastest way (if possible in the browser thanks to an online tool, or if not possible easily, with Python), to get the frequency response curve (x-axis: Hz, y-axis: dB), when giving just: ...
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285 views

What does the amplitude in a frequency response of a signal signify?

Well according to my understanding it tells the concentration of signals at a particular frequency but what does the number really mean? Suppose in a frequency response graph i have such a relation :: ...
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3-tap FIR filter: simple expression for $H(e^{j\omega})$ using trigonometric identities

We have a linear time-invariant system described by the input-output relation $$y[n] = x[n] + 2x[n - 1] + x[n - 2]$$ Below is my approach to analyze this system. The impulse response of this system ...
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How to calculate the frequency response of LTI system based on measured impedance

I have an analog circuit containing unknown resistance, capacitance, and inductance. I have measured its complex impedance across the frequency range of interest. Is there an equation that will allow ...
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338 views

Z Transform - Do i always need 2 poles for every “peak”?

I am quite new to digital signal processing (and also Z transforms). I am reading about frequency response modelling and have some questions do we always need a pair of poles for each "peak" in the ...
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Relationship between the Real and Imaginary parts of a LTI causal system

Prelude I am writing an elaborate text on the relationship between the real and imaginary parts of a LTI causal system and how stability, causality and analyticity imposes various constraints on its ...
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Phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$

I want to find the phase plot of $H(e^{j\omega})=(1-re^{-j\omega})\left(1-\dfrac{1}{r}e^{-j\omega}\right)$, $0<r<1$ for the interval $0\leq \omega \leq \pi$. Method 1: $H(e^{j\omega})=1-\left(...
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real refractive index from Kramers Kronig relation

I have a measurement of the complex part of the refractive index $k$ (where the refractive index is $m = n + i\,k$) measured at a nonlinear grid of wavelengths or frequencies that span several orders ...
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Impulse response from Frequency response: why using $e^{j\omega}$ as an input?

Every resource that I can find uses this identity when deriving impulse response: $h[n] = IDTFT \Big\{H(e^{j\omega}) \Big\}$ Suggesting that the input signal was $e^{j\omega}$. But by definition ...
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Phase wrap when computing impulse response from frequency response [closed]

Short: I have the frequency response of a system as a set of complex numbers. I want the impulse response for that system. Problem: The phase of my frequency response wraps around 2pi multiple times....
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Approximate a System Frequency Response with a Filter in MATLAB

suppose I know the frequency response of a (linear) model approximating a real physical system but only at a specific frequency $f_0$ (so basically I have a complex number whose module is the ...
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How to make semilogx to get a plot gain against log frequency with several values? [beginner] [closed]

Gain: 20 log (Vout/Vin) with Vin = 1.0. I've been searching for gain values: a. -156.48 dB b. -80 dB c. -53.98 dB d. -13.98 dB e. 3.52 dB f. 10.32 dB g. 13 dB h. 13.93 dB i. 13.96 dB j. 13.98 dB I am ...
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How do I generate sine waves with MATLAB’s max operator and the plot the resulting values in dB versus log frequency? [closed]

I just start learning about matlab. Im very confuse with this. Can anyone gives me such an example solution or any kind of help? HINT: Put the desired input frequencies in an array and use a for-loop ...
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digital low pass Butterworth filter

A digital low pass Butterworth filter that has been designed using Bi-linear transformation has been a pole at $z=0.6$. It is also known that the filter's attenuate (at digital frequency) $\omega = 1....
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Butterworth High Pass Filter Amplitude Response

I have learned the Butterworth filter, normally it is used for low pass design. And the amplitude response is: $$|H(jw)|=\frac{1}{\sqrt{1+(\frac{w}{w_{c}})^{2n}}}$$ mentioned in this Butterworth ...
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Butterworth filter approximation: derivation and output poles

I am having trouble understanding the exact derivation of the butterworth filter and how it results in the output of the poles. I have researched multiple lecture series and textbooks and this is my ...
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Reconciling Continuous and Discrete Complex Domains

Having taken some courses in Systems and Stability dealing mostly with continuous time signals, I am accustomed to thinking about the Laplace and Fourier transforms dealing with complex and pure ...
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The desired frequency-response specifications

The complex function $ D (e^{-jw})$ is defined on the domain of approximation $\Omega$ .In most cases the domain $\Omega$ is the union of several disjoint frequency bands which are separated by ...
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How to compute the impulse response from incomplete frequency response data?

I need to compute the impulse response of a system, but I only have access to the frequency response data. This data contains the output magnitude of the system (for a fixed input amplitude) at ...
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761 views

Shelving filter (2nd order)

I'm trying to find the equation of a shelving filter of the second order. I easily found the equation for a first order filter on wikipedia with a transition region which have a 6db per octave slope. ...
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Given a log-plot of frequency-magnitude-phase how to apply it as an EQ curve to a signal?

I have several hundred data points that represents an EQ correction curve, where each point contains frequency, magnitude, and phase (-1..+1). The frequencies are distributed exponentially, not ...
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How to evaluate CCDE at a given frequency?

Consider the following Constant Coefficient Difference Equation (CCDE) given below $$y[n] - \frac{1}{2}y[n-1] = 2x[n] - 5x[n-1] - x[n-2]$$ Let $H(e^{j\omega})$ denote the transfer function of this ...
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Making longer a time domain signal by adding values on its frequency domain. What am I doing wrong?

Background Here's the thing: using software for Finite Element Acoustic Simulation I got the dataset of frequency response from a room; software works by solving the wave equation in the interval $`[...
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Frequency response of marginally stable LTI systems

The frequency response of a system is defined as: $$\int_0^\infty{h(t)e^{-j\omega t}dt}$$ where $h(t)$ is the impulse response. But in marginally stable systems, $h(t)$ does not decay so the integral ...
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Equalize Speaker using impulse response

So I have this school project where my aim is to improve a loudspeaker in general, my idea is to mesure the impulse response of the room using a mic, then use this mesure to conceive a loudspeaker ...
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Evauating response to $x(n) = \sin{2\pi\frac{1}{4}n}$ given the system function

Let the input signal $x(n) = \sin{2\pi\frac{1}{4}n}$ go in to the system described by: $$y(n) - y(n-1)+\frac{3}{16}y(n-2) =x(n).$$ What is the output signal? I've calculated the system function $H(...
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Homework Help: What does $h[0] = 1$ represent? What is $\ln \big| H(e^{j \omega})\big|$?

I have been staring at this problem for a week now... Suppose $H(e^{j \omega})$ is the frequency response of a stable and causal minimum-phase discrete-time system with $h[0]=1$ ($h[n]$ is the ...
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Effect of sampling frequency to the center of a bandbass filter

Is it true that if you have some sort of filter, e.g. a digital bandpass filter around the frequency 1000 Hz that is given in the form of a transfer function $H(z)$ and you then change the sampling ...
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Phase function of filter

I have a filter with the transfer function $$H(z) = 1 - 2z^{-2} + z^{-4}.$$ The task is to find the phase function $\theta (\omega).$ My attempt is to start by expressing the frequency response \...
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Why are numerator coefficients named $b$ and denominator coefficients named $a$?

This is not a technical question, it is rather a question about the implicit notation used in MATLAB and some digital signal processing books to refer to the numerator and denominator coefficients of ...
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Difference between $H(\omega)$ and $H(j\omega)$ [duplicate]

What is the difference between $H(\omega)$ and $H(j\omega)$, in terms of impulse response. And if so, when do I have to use one or another.

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